FACT++  1.0
ld.c
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1 #include "erfa.h"
2 
3 void eraLd(double bm, double p[3], double q[3], double e[3],
4  double em, double dlim, double p1[3])
5 /*
6 ** - - - - - -
7 ** e r a L d
8 ** - - - - - -
9 **
10 ** Apply light deflection by a solar-system body, as part of
11 ** transforming coordinate direction into natural direction.
12 **
13 ** Given:
14 ** bm double mass of the gravitating body (solar masses)
15 ** p double[3] direction from observer to source (unit vector)
16 ** q double[3] direction from body to source (unit vector)
17 ** e double[3] direction from body to observer (unit vector)
18 ** em double distance from body to observer (au)
19 ** dlim double deflection limiter (Note 4)
20 **
21 ** Returned:
22 ** p1 double[3] observer to deflected source (unit vector)
23 **
24 ** Notes:
25 **
26 ** 1) The algorithm is based on Expr. (70) in Klioner (2003) and
27 ** Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann
28 ** 2013), with some rearrangement to minimize the effects of machine
29 ** precision.
30 **
31 ** 2) The mass parameter bm can, as required, be adjusted in order to
32 ** allow for such effects as quadrupole field.
33 **
34 ** 3) The barycentric position of the deflecting body should ideally
35 ** correspond to the time of closest approach of the light ray to
36 ** the body.
37 **
38 ** 4) The deflection limiter parameter dlim is phi^2/2, where phi is
39 ** the angular separation (in radians) between source and body at
40 ** which limiting is applied. As phi shrinks below the chosen
41 ** threshold, the deflection is artificially reduced, reaching zero
42 ** for phi = 0.
43 **
44 ** 5) The returned vector p1 is not normalized, but the consequential
45 ** departure from unit magnitude is always negligible.
46 **
47 ** 6) The arguments p and p1 can be the same array.
48 **
49 ** 7) To accumulate total light deflection taking into account the
50 ** contributions from several bodies, call the present function for
51 ** each body in succession, in decreasing order of distance from the
52 ** observer.
53 **
54 ** 8) For efficiency, validation is omitted. The supplied vectors must
55 ** be of unit magnitude, and the deflection limiter non-zero and
56 ** positive.
57 **
58 ** References:
59 **
60 ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
61 ** the Astronomical Almanac, 3rd ed., University Science Books
62 ** (2013).
63 **
64 ** Klioner, Sergei A., "A practical relativistic model for micro-
65 ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
66 **
67 ** Called:
68 ** eraPdp scalar product of two p-vectors
69 ** eraPxp vector product of two p-vectors
70 **
71 ** Copyright (C) 2013-2015, NumFOCUS Foundation.
72 ** Derived, with permission, from the SOFA library. See notes at end of file.
73 */
74 {
75  int i;
76  double qpe[3], qdqpe, w, eq[3], peq[3];
77 
78 /* q . (q + e). */
79  for (i = 0; i < 3; i++) {
80  qpe[i] = q[i] + e[i];
81  }
82  qdqpe = eraPdp(q, qpe);
83 
84 /* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */
85  w = bm * ERFA_SRS / em / ERFA_GMAX(qdqpe,dlim);
86 
87 /* p x (e x q). */
88  eraPxp(e, q, eq);
89  eraPxp(p, eq, peq);
90 
91 /* Apply the deflection. */
92  for (i = 0; i < 3; i++) {
93  p1[i] = p[i] + w*peq[i];
94  }
95 
96 /* Finished. */
97 
98 }
99 /*----------------------------------------------------------------------
100 **
101 **
102 ** Copyright (C) 2013-2015, NumFOCUS Foundation.
103 ** All rights reserved.
104 **
105 ** This library is derived, with permission, from the International
106 ** Astronomical Union's "Standards of Fundamental Astronomy" library,
107 ** available from http://www.iausofa.org.
108 **
109 ** The ERFA version is intended to retain identical functionality to
110 ** the SOFA library, but made distinct through different function and
111 ** file names, as set out in the SOFA license conditions. The SOFA
112 ** original has a role as a reference standard for the IAU and IERS,
113 ** and consequently redistribution is permitted only in its unaltered
114 ** state. The ERFA version is not subject to this restriction and
115 ** therefore can be included in distributions which do not support the
116 ** concept of "read only" software.
117 **
118 ** Although the intent is to replicate the SOFA API (other than
119 ** replacement of prefix names) and results (with the exception of
120 ** bugs; any that are discovered will be fixed), SOFA is not
121 ** responsible for any errors found in this version of the library.
122 **
123 ** If you wish to acknowledge the SOFA heritage, please acknowledge
124 ** that you are using a library derived from SOFA, rather than SOFA
125 ** itself.
126 **
127 **
128 ** TERMS AND CONDITIONS
129 **
130 ** Redistribution and use in source and binary forms, with or without
131 ** modification, are permitted provided that the following conditions
132 ** are met:
133 **
134 ** 1 Redistributions of source code must retain the above copyright
135 ** notice, this list of conditions and the following disclaimer.
136 **
137 ** 2 Redistributions in binary form must reproduce the above copyright
138 ** notice, this list of conditions and the following disclaimer in
139 ** the documentation and/or other materials provided with the
140 ** distribution.
141 **
142 ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
143 ** the International Astronomical Union nor the names of its
144 ** contributors may be used to endorse or promote products derived
145 ** from this software without specific prior written permission.
146 **
147 ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
148 ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
149 ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
150 ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
151 ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
152 ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
153 ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
154 ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
155 ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
156 ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
157 ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
158 ** POSSIBILITY OF SUCH DAMAGE.
159 **
160 */
eraPdp
double eraPdp(double a[3], double b[3])
Definition: pdp.c:3
ERFA_SRS
#define ERFA_SRS
Definition: erfam.h:122
ERFA_GMAX
#define ERFA_GMAX(A, B)
Definition: erfam.h:134
i
int i
Definition: db_dim_client.c:21
eraLd
void eraLd(double bm, double p[3], double q[3], double e[3], double em, double dlim, double p1[3])
Definition: ld.c:3
eraPxp
void eraPxp(double a[3], double b[3], double axb[3])
Definition: pxp.c:3